MONTREAL -- Canada on Thursday sought to break a logjam in overhauling the North American Free Trade Agreement by introducing a proposal for more North American content in automobiles, according to people following the talks.

Ottawa's informal proposal is in response to a U.S. demand for significant increases in the share of a car and its parts that must be made in one of the three countries party to the deal -- which also includes Mexico -- to be eligible for duty-free trade.

The U.S. has said it wants to increase North American car content from the current 62.5% to 85%. The purpose is to prevent Asian or other overseas content from expanding in the North American supply chain.

The proposal is the latest signal that Canada and Mexico are aiming to show flexibility and engage with U.S. negotiators at the bargaining table. U.S. President Donald Trump has threatened to withdraw from Nafta if the three countries don't agree on a major overhaul.

Before the current round of talks in Montreal, the countries haven't notched any progress on the auto rules or several other issues that divide the U.S. from its neighbors. This week, negotiators have made some progress on less-controversial chapters, according to people briefed on the talks, meaning that portions of the pact that address telecommunications, anticorruption, and technical barriers to trade could be virtually complete at the end of this round, one of these people said.

Responding to U.S. demands for more North American car content, Canada proposed broadening the definition of what should be counted to include software, other technological components now common in cars, and raw materials like steel and aluminum. U.S. officials welcomed the proposal and indicated they would look at it closely, according to two people briefed on the talks.

Canada hopes its offer will encourage the U.S. to moderate its demands, according to an official.

But Canada's proposal didn't address arguably the most contentious element in the entire Nafta negotiations -- that specifically U.S.-made components make up half of the parts used to build light vehicles in North America to qualify for duty-free movement.

Jerry Dias, president of Unifor, Canada's largest private-sector union, said talks on autos are headed in the right direction. However, he said, "there will be no Nafta" unless the Trump administration drops its demand for cars to contain 50% U.S. parts.

Canada's chief negotiator, Steve Verheul, told reporters talks were "reasonably constructive," without elaborating. A spokeswoman for U.S. Trade Representative Robert Lighthizer declined to comment. Kenneth Smith, Mexico's chief negotiator, said the countries are making "good technical progress" and it is analyzing the proposal made by Canada.

Meanwhile, Mr. Lighthizer and Canadian Foreign Minister Chrystia Freeland met in Davos, Switzerland, on the sidelines of the World Economic Forum, according to a Canadian official. At the meeting, Mr. Lighthizer asked about Canada's fresh approach on cars, the official said.

Canada's approach on the thorny auto issue has earned praise from the car industry, including from Sergio Marchionne, chief executive of Fiat Chrysler Automobiles NV. He told analysts during a conference call Thursday he was "encouraged" by events unfolding in Montreal, but warned of broader economic repercussions if the U.S. pressed ahead with demands in an effort to get factories in Mexico to relocate to the U.S.

The North American auto industry has repeatedly warned the Trump administration that tightening the rules of origin on cars' content too much could backfire and send some production overseas. But like other industries, auto makers are also worried that a rift at the negotiating table could spell the end of Nafta if Mr. Trump follows through with threats to withdraw from the 24-year-old pact.

"Any step back from the precipice is a good thing," said John Bozello, chief executive of Global Automakers, which represents international producers that build or sell cars in the U.S.

"I think Canada should be congratulated for putting some of those concepts forward," said Ann Wilson, senior vice president at the Motor and Equipment Manufacturers Association, which represents the auto-parts industry.

Significant differences remain, including over how trade disputes among the Nafta countries are resolved; demands from the U.S. that Canada dismantle its system that protects dairy farmers from imports; limits the U.S. wants to impose on access to its government-procurement market; and a U.S. request for a so-called sunset clause that would allow a country to terminate the pact every five years.

In Davos, Canadian Prime Minister Justin Trudeau told reporters he is confident the negotiations can succeed. "I know we will be able to get there," Mr. Trudeau said.

Also in Davos, Bank of Canada Governor Stephen Poloz said uncertainty over Nafta is already posing a drag on the economy, and reiterated that the pact's dissolution represents the Canadian economy's top downside risk.

--Chester Dawson in Detroit contributed to this article.

Write to Paul Vieira at paul.vieira@wsj.com and William Mauldin at william.mauldin@wsj.com